Within the last year
Within the past 3 years
1 - 10 of 18 articles
Let n = n 1 + n 2 + … + n j a partition Π of n . One will say that this partition represents the integer a if there exists a subsum n i l + n i 2 + … + n i l equal to a. The set E (Π) is defined as the set of all integers a represented by Π. Let A be a subset of the set of positive...
A Behrend sequence is a (necessarily infinite) integer sequence A with elements exceeding 1 and whose set of multiples M A ) has logarithmic density μ( A ) = 1. By a famous theorem of Davenport and Erdös, this implies that ( M A ) also has natural density equal to 1. An ϵ-pseudo-Behrend...
This paper determines lower bounds on the number of different cycle lengths in a graph of given minimum degree k and girth g . The most general result gives a lower bound of ck g /8 .
It is known that for sufficiently large n and m and any r the binomial coefficient ( n m ) which is close to the middle coefficient is divisible by p r where p is a ‘large’ prime. We prove the exact divisibility of ( n m ) by p r for p > c ( n ). The lower bound is essentially the best...
We say ( n , e ) → ( m , f ), an ( m, f ) subgraph is forced, if every n -vertex graph of size e has an m -vertex spanned subgraph with f edges. For example, as Turán proved, ( n , e )→( k ,( k 2 )) for e > t k − 1 ( n ) and (n,e) ↛( k 2 )) , otherwise. We give a number of constructions...
Let m ( n ) denote the smallest integer m with the property that any set of n points in Euclidean 3-space has an element such that at most m other elements are equidistant from it. We have that cn 1/3 log log n ⩽ m ( n ) ⩽ n 3/5 β ( n ), where c > 0 is a constant and β ( n ) is an extremely...
We study the distribution of lattice points a + 1 b on the fixed circle a 2 + b 2 = n . Our results apply p.p. to the representable integers n , and we supply bounds for the discrepancy of the distribution, and for the maximum and minimum of the angles between consecutive points. As a corollary,...
We consider a number of density problems for integer sequences with certain divisibility properties and sequences free of arithmetic progressions. Sequences of the latter type that are generated by a computer using modifications of the greedy algorithm are also provided.
Read and print from thousands of top scholarly journals.
Sign up with Facebook
Sign up with Google
Already have an account? Log in
Save this article to read later. You can see your Read Later on your DeepDyve homepage.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Sign Up Log In
To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.
To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.